`ax^(n)+be^(x)+c sin x`

f(x)={(a^(x)-1)/(x^(n)sin x)((b sin x-sin bx)/(cos x-cos bx))^(n)x>0 and (a^(x)sin bx-b^(x)sin ax)/(tan ax)x 0,b!=1,a!=b). obtain f(0) and a relation between a,b and n.

Consider lim (ax+be^(-x)+sin x+1)/(ax-b sin x)=l(1 is finite) then

In the equation int (dx)/sqrt(2ax - x^(2) ) = a^(2) sin ^(-1) [(x)/(a) - 1] . Find the value of n .

Show that sum_(k =0)^(n) C_(k) *sin (kx) cos (n-k) x = 2^(n-1)sin n x where C_(r )= ""^(n)C_(r )

If I_(n)=int x^(n)cos axdx and I_(n)=int x^(n)sin axdx then show that.(1)aI_(n)=x^(n)sin ax-nI_(n-1)

The value of int(ax^(2))/(x sqrt(c^(2)x^(2)-(ax^(2)+b)^(2)))(1)/(c)sin^(-1)(ax+(b)/(x))+k csin^(-1)(a+(b)/(x))+esin^(-1)((ax+(b)/(x))/(c))+k( d) none of these